Find the parallel line of y=1/2x that passes through the point (-3, 4).
Understand the Problem
The question is asking us to find the equation of a line that is parallel to the line given by y=1/2x and passes through the point (-3, 4). To do this, we need to use the fact that parallel lines have the same slope.
Answer
$$ y = \frac{1}{2}x + \frac{11}{2} $$
Answer for screen readers
The equation of the line parallel to $y = \frac{1}{2}x$ that passes through the point $(-3, 4)$ is given by:
$$ y = \frac{1}{2}x + \frac{11}{2} $$
Steps to Solve
- Identify the slope of the given line
The equation of the given line is $y = \frac{1}{2}x$.
The slope (m) of this line is $\frac{1}{2}$. Since parallel lines have the same slope, our new line will also have a slope of $\frac{1}{2}$.
- Use point-slope form for the equation of the line
We can use the point-slope form of the line, which is given by:
$$ y - y_1 = m(x - x_1) $$
Where $(x_1, y_1)$ is the point the line passes through, and $m$ is the slope.
Substituting $m = \frac{1}{2}$ and the point $(-3, 4)$ into the equation:
$$ y - 4 = \frac{1}{2}(x + 3) $$
- Simplify the equation
Now, distribute and solve for $y$:
$$ y - 4 = \frac{1}{2}x + \frac{3}{2} $$
Add 4 to both sides:
$$ y = \frac{1}{2}x + \frac{3}{2} + 4 $$
Convert 4 to halves:
$$ 4 = \frac{8}{2} $$
So:
$$ y = \frac{1}{2}x + \frac{3}{2} + \frac{8}{2} $$
Combine like terms:
$$ y = \frac{1}{2}x + \frac{11}{2} $$
This is the equation of the line parallel to the given line that passes through the point (-3, 4).
The equation of the line parallel to $y = \frac{1}{2}x$ that passes through the point $(-3, 4)$ is given by:
$$ y = \frac{1}{2}x + \frac{11}{2} $$
More Information
This equation represents a line with a slope of $\frac{1}{2}$, which means for every 2 units you move to the right on the x-axis, the line moves up 1 unit on the y-axis. This line will never intersect the line $y = \frac{1}{2}x$ because they are parallel.
Tips
- Forgetting to use the point-slope form correctly: It's crucial to substitute both the slope and the point accurately into the equation.
- Not simplifying the constant term correctly, leading to an incorrect final expression.
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